Finite Group DatabasebetaFinite Group Databasebeta| order | 35972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×D529 |
| unambiguous semidirect product | C529⋊(C22×C17) |
| unambiguous semidirect product | (C2×C529)⋊(C2×C17) |
| Fitting | C2×C17×C529 ⋊ C2 |
| derived, Sylow | C529 ⋊ C22×C17 |
| Hall | C17×C529 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D529 |
| commutator, cosocle, hypocenter | C529 | C22×C17 |
| Frattini | C23 | C2×C17×D23 |
| Fitting | C2×C17×C529 | C2 |
| socle | C2×C17×C23 | D23 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C2×C17 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17986 |
9044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35972, 9);